I was replacing the start capacitor on my 7.5 hp compressor. On the 220V motor was also a Stearns SINPAC switch. I checked online on how to test it but I don't know what it is for and what are the symptoms of a faulty one? Any response would be appreciated.

It looks like the SINPAC is a start assist relay that cuts out because of back emf. To check it, measure current in the start winding. It should start high and drop to zero after a short time, like 1 second. If the motor won't start and there is no current in the start winding, bad switch. If the start winding always has current, bad switch.